The notion of phoneme is sufficiently abstract that many
students have a hard time getting hold of just when you have two diffierent
phonemes, and when youre looking at allophones. The idea of distributions
or environments seems obvious to us. Of course, these environments are
defined by the properties of the sounds/signs around them, and the distribution
of an allophone is the set of the environments where that allophone occurs.
But remember that your students may be just learning about how to define
the linguistic properties of a sound or a manual sign. Understanding in
what terms to define the environments will not come automatically to them,
as they may be struggling to keep the differences between features, allophones
and phonemes straight, not to mention where each of these terms is relevant.

(1) Here are a few ways of expressing a definition of complementary distribution.
They all require you to explain some background. For example, what does
mutually exclusive mean? segment? distribution?

(2) Complementary distribution is the mutually exclusive relationship
between two phonetically similar segments. It exists when one segment
occurs in an environment where the other segment never occurs.
Relation between sounds or forms whose distributions do not overlap. Thus
in southern British English (RP), an unaspirated [p] appears after an
initial [s], e.g. in [spin] (spin); an aspirated [ph] e.g. initially in
[ph i n]; but there is no context in which both would be normal. Therefore
they are in complementary distribution, and therefore, in part, they are
described as allophones of the same phoneme.

(3) Think about a soccer team: Each player standing on the field has
her own environment where she waits for the kickoff. This
environment is the territory where she launches an offensive strategy,
and the territory that she defends when the opposite team is approaching
her teams goal. She may be the goalie, or the fullback, or right
halfback. Her position or territory is defined relative to the center
line and right or left halves of the field, or relative to her teams
goal. Any single player with any of these territories is not the team
 the team is the whole collection of players with their territories.
Think of the phoneme like the team, and the allophones like the players.
Allophones also have their territory or linguistic environments
that they cover, and no allophones of a phoneme will have overlapping
territories. These territories, or environments, are defined
in terms of the relevant linguistic features of the sounds near the allophone.
These relevant linguistic features are features related to
voicing, place and manner of the sounds, or handshape, location, and orientation
of a signed segment. When one sound or signed segment enters the territory
of another, you know they are on opposing teams, i.e., members of different
phonemes. When you define the territory of an allophone, you are defining
its distribution, the set of places within words in a language where the
allophone appears.

Here is an example:

* [spæt] [phæt] *[sphæt] *[pæt]
* [spul] [phul] *[sphul] *[pul]
[ph] and [p] are in complementary distribution. [p], or unaspirated
p, doesnt occur word-initially, but aspirated p
does. An English speaker hears these sounds as the same sound; even if
some speakers pronounce words with unaspriated [p] at the beginning, other
speakers wont hear those pronunciations as different words with
different meanings.

Distribution:
The set of contexts within sentences or within words in which a unit or
class of units can appear. For example, nouns can fill certain contexts
within sentences; these contexts can be defined as a set of grammatical
roles like subject or object. The contexts for allophones
can be defined in terms of features of the sounds around them, or properties
of syllables or words. For example, word-initial or syllable-final;
after consonants or before vowels; before
voiced fricatives or after front vowels.